Tethering is the practice of using a mobile device (such as a smartphone) as a modem to connect another device, such as a laptop or another mobile phone to the Internet. To do so, the phone must have mobile data enabled.
Tethering is one method of creating a mobile hotspot (an ad hoc wireless access point). The practice is increasingly common for travelers, out-of-office employees and those who want access to an alternative to the corporate network from within the workplace. (See: BYON -- bring your own network.) Tethering may or may not provide affordable connectivity, depending on the user's data plan and contract.
A tether is a long leash. In phone tethering, the leash is either a USB cable or a wireless Bluetooth connection.